Some research said the multi-axial rupture is governed by Von-Mises stress, some others said it is governed by principal stress? Does anyone know the reason behind?
Thank you very much!
Study these sources. The most comprehensive explanation of the multiaxial phenomena.
(1) Novozhilov, V.V.: Theory of Elasticity. Oxford: Pergamon Press 1961
(2) Zenner, H., I. Richter : Eine Festigkeitshypothese für die Dauerfestigkeit bei beliebigen Bean-spruchungskombinationen. Konstruktion 29 (1977) H.1, S.11-28
(3) Heidenreich, R., W. Schütz, I. Richter, H. Zenner: Schubspannungsintensitätshypothese - Dauerfestigkeit bei mehrachsiger Beanspruchung. Abschlußbericht zum Vorhaben Nr.59, FKM-Heft 105, Forschungskuratorium Maschinenbau (1983)
(4) Liu, J.: Beitrag zur Verbesserung der Dauerfestigkeitsberechnung bei mehrachsiger Bean-spruchung. Dissertation TU Clausthal (1991)
When considering creep under a multiaxial stress state, primary creep is dependent on von-Mises stress where as the mechanisms which govern tertiary creep can be dependent on both von-Mises and principle stresses. Some alloys such as Ti alloys display less dependence on max principle stress than others such as Ni-based alloys which are strongly dependent on loading direction. This paper may help:
http://rspa.royalsocietypublishing.org/content/456/1996/835.full.pdf
To add a little to what William Harrison has given: Consider the case of equi-biaxial tension, where two principal stresses are equal and the third is zero. If you calculate the von Mises stress for this condition you will find that the von Mises and maximum principal stresses are equal just as they are for the uniaxial case. This would suggest that a stress in two directions has exactly the same effect as a single stress in only one direction. I have not seen any data to support this conclusion. The life is always much shorter for this case. Furthermore, this is actually a very common state of stress in real engineering cases and is therefore very important to get the predictions right for this case. Nevertheless, there is a solution, which is that multiaxial rupture is governed by (i) the von Mises stress (ii) the maximum principal stress and (iii) the hydrostatic or mean stress. See below for an example:
The other factor you should bear in mind is that multiaxial creep tests are usually constant load and different states of stress increase the true von Mises Stress differently for the same increase in von Mises strain. This can often mislead researchers into overestimating the importance of the maximum principal stress. It is best to have constant stress multiaxial data, but this is rare, so convert to constant stress conditions before making the comparisons.
Article The multiaxial creep ductility of austenitic stainless steels
As per my understanding
Stress field in a component is having two components 1. Hydrostatic 2 devitorial
von Mises is devitorial part and is responsible for deformations in low temperature zone due to slip. As temperature increases to creep zone, mechanism of deformation/damage is contributed by diffusion also. In multiaxial stress state if triaxiality is high, rupture will be accelerated, because now hydrostatic stresses are also helping in damage.
In the paper of Sdobyrev as well as in several papers published by Leckie and Hayhurst multi-axial data on creep rupture for many materials were collected. The data show that for materials like aluminum the time to creep rupture correlates with the von Mises equivalent stress, while for materials like pure copper the maximum tensile stress (first positive principal stress) should applied. For many isotropic materials a mixture rule (a linear combination of von Mises equivalent stress, first positive principal stress and hydrostatic stress) can be used as a simple phenomenological criterion. As Michael Spindler pointed out, a stress based creep rupture criterion may be misleading if strains are essential (over 10%), since the Cauchy stress tensor changes over time.
In my view it is more accurate to consider creep damage as a process, and to formulate a kinetic equation. For many materials the damage rate (for example growth of cavities) is related to the equivalent creep rate (it depends primarily on the von Mises equivalent stress).. The cavity nucleation, coalescence and formation of micro-cracks can be related to the first positive principal stress. These facts are well documented in many experimental works and recently, based on micro-mechanical simulations.
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